Optical designs for non-deterministic turing machines

The construction of an optical computer that can explore the computation tree of a non-deterministic Turing machine in the time it takes to explore one path of the computation has been described in Dolev and Nir 2003. In this paper, we elaborate on the design considerations of Dolev and Nir 2003. The construction of such an optical computer will allow solving NP problems in polynomial time. The limitation is space, where every beam location (hitting a prism) represents a different Turing machine configuration. By the use of writable (holographic) memory, we are able to reduce the space only by a constant factor. Tradeoffs between the use of semantics for each location in space, and the use of digital storage is discussed. In the writable model, configurations can be represented in binary (or higher base digital) representation, rather than mapping each location in space to a single configuration. We show that, the benefit of such a digital representation in the scope of concurrent exhaustive search is limited.